{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:5X2XPKGIIKH77XUY57PZUA5R3B","short_pith_number":"pith:5X2XPKGI","canonical_record":{"source":{"id":"1502.04939","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-02-17T16:00:26Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"749eb87d41d9c1ce97eab58b45ef7d5f7c9d1473da47d599ee242f305854e4cf","abstract_canon_sha256":"f45278bec91c4e6d5d94dffc021838146a422af6db5591bbb04e2e5661c92540"},"schema_version":"1.0"},"canonical_sha256":"edf577a8c8428fffde98efdf9a03b1d851144dad3c6c265a879156b269256afe","source":{"kind":"arxiv","id":"1502.04939","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04939","created_at":"2026-07-05T02:02:48Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04939v3","created_at":"2026-07-05T02:02:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04939","created_at":"2026-07-05T02:02:48Z"},{"alias_kind":"pith_short_12","alias_value":"5X2XPKGIIKH7","created_at":"2026-07-05T02:02:48Z"},{"alias_kind":"pith_short_16","alias_value":"5X2XPKGIIKH77XUY","created_at":"2026-07-05T02:02:48Z"},{"alias_kind":"pith_short_8","alias_value":"5X2XPKGI","created_at":"2026-07-05T02:02:48Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:5X2XPKGIIKH77XUY57PZUA5R3B","target":"record","payload":{"canonical_record":{"source":{"id":"1502.04939","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-02-17T16:00:26Z","cross_cats_sorted":["math.GT"],"title_canon_sha256":"749eb87d41d9c1ce97eab58b45ef7d5f7c9d1473da47d599ee242f305854e4cf","abstract_canon_sha256":"f45278bec91c4e6d5d94dffc021838146a422af6db5591bbb04e2e5661c92540"},"schema_version":"1.0"},"canonical_sha256":"edf577a8c8428fffde98efdf9a03b1d851144dad3c6c265a879156b269256afe","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:02:48.359611Z","signature_b64":"JQiNFbYs+rpYfLrvHZ09gHjM82j/n59QtTmQX+iR6hLJBFJqsJAEhYMBsMBHIyOlUuTkgeuqmatmcGwJDYLECQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"edf577a8c8428fffde98efdf9a03b1d851144dad3c6c265a879156b269256afe","last_reissued_at":"2026-07-05T02:02:48.359222Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:02:48.359222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1502.04939","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:02:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"iE7IRyk5EtiFqpIuFAbXytoXKnszdfINLEvE6shs3j7TbfVqjgKhq/llSBAu4kAIEPDRz19fW/Ad5/RTyrALDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:59:31.286841Z"},"content_sha256":"a3fd79d01a66d9ccd5c0a235c1ef1cc530681b0b0438e5ecee57467cbef3c9af","schema_version":"1.0","event_id":"sha256:a3fd79d01a66d9ccd5c0a235c1ef1cc530681b0b0438e5ecee57467cbef3c9af"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:5X2XPKGIIKH77XUY57PZUA5R3B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Augmentations are Sheaves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.SG","authors_text":"Dan Rutherford, Eric Zaslow, Lenhard Ng, Steven Sivek, Vivek Shende","submitted_at":"2015-02-17T16:00:26Z","abstract_excerpt":"We show that the set of augmentations of the Chekanov-Eliashberg algebra of a Legendrian link underlies the structure of a unital A-infinity category. This differs from the non-unital category constructed in [BC], but is related to it in the same way that cohomology is related to compactly supported cohomology. The existence of such a category was predicted by [STZ], who moreover conjectured its equivalence to a category of sheaves on the front plane with singular support meeting infinity in the knot. After showing that the augmentation category forms a sheaf over the x-line, we are able to pr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04939","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1502.04939/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:02:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4TsrfpeSvkc28PoLrIK4BRfJ2GIT3OqsUXUhe8IYz9+An4wnzbAGTZmKmRSleRwsXGbtbmAoFKB8l8UjoIBwCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-16T10:59:31.287537Z"},"content_sha256":"ad7a0ce2ae18b52d7033600cbe2e34f7119b26593a00f448e47f3ae2c92d3217","schema_version":"1.0","event_id":"sha256:ad7a0ce2ae18b52d7033600cbe2e34f7119b26593a00f448e47f3ae2c92d3217"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5X2XPKGIIKH77XUY57PZUA5R3B/bundle.json","state_url":"https://pith.science/pith/5X2XPKGIIKH77XUY57PZUA5R3B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5X2XPKGIIKH77XUY57PZUA5R3B/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-08-16T10:59:31Z","links":{"resolver":"https://pith.science/pith/5X2XPKGIIKH77XUY57PZUA5R3B","bundle":"https://pith.science/pith/5X2XPKGIIKH77XUY57PZUA5R3B/bundle.json","state":"https://pith.science/pith/5X2XPKGIIKH77XUY57PZUA5R3B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5X2XPKGIIKH77XUY57PZUA5R3B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:5X2XPKGIIKH77XUY57PZUA5R3B","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"f45278bec91c4e6d5d94dffc021838146a422af6db5591bbb04e2e5661c92540","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-02-17T16:00:26Z","title_canon_sha256":"749eb87d41d9c1ce97eab58b45ef7d5f7c9d1473da47d599ee242f305854e4cf"},"schema_version":"1.0","source":{"id":"1502.04939","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1502.04939","created_at":"2026-07-05T02:02:48Z"},{"alias_kind":"arxiv_version","alias_value":"1502.04939v3","created_at":"2026-07-05T02:02:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1502.04939","created_at":"2026-07-05T02:02:48Z"},{"alias_kind":"pith_short_12","alias_value":"5X2XPKGIIKH7","created_at":"2026-07-05T02:02:48Z"},{"alias_kind":"pith_short_16","alias_value":"5X2XPKGIIKH77XUY","created_at":"2026-07-05T02:02:48Z"},{"alias_kind":"pith_short_8","alias_value":"5X2XPKGI","created_at":"2026-07-05T02:02:48Z"}],"graph_snapshots":[{"event_id":"sha256:ad7a0ce2ae18b52d7033600cbe2e34f7119b26593a00f448e47f3ae2c92d3217","target":"graph","created_at":"2026-07-05T02:02:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1502.04939/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We show that the set of augmentations of the Chekanov-Eliashberg algebra of a Legendrian link underlies the structure of a unital A-infinity category. This differs from the non-unital category constructed in [BC], but is related to it in the same way that cohomology is related to compactly supported cohomology. The existence of such a category was predicted by [STZ], who moreover conjectured its equivalence to a category of sheaves on the front plane with singular support meeting infinity in the knot. After showing that the augmentation category forms a sheaf over the x-line, we are able to pr","authors_text":"Dan Rutherford, Eric Zaslow, Lenhard Ng, Steven Sivek, Vivek Shende","cross_cats":["math.GT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-02-17T16:00:26Z","title":"Augmentations are Sheaves"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.04939","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:a3fd79d01a66d9ccd5c0a235c1ef1cc530681b0b0438e5ecee57467cbef3c9af","target":"record","created_at":"2026-07-05T02:02:48Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"f45278bec91c4e6d5d94dffc021838146a422af6db5591bbb04e2e5661c92540","cross_cats_sorted":["math.GT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SG","submitted_at":"2015-02-17T16:00:26Z","title_canon_sha256":"749eb87d41d9c1ce97eab58b45ef7d5f7c9d1473da47d599ee242f305854e4cf"},"schema_version":"1.0","source":{"id":"1502.04939","kind":"arxiv","version":3}},"canonical_sha256":"edf577a8c8428fffde98efdf9a03b1d851144dad3c6c265a879156b269256afe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"edf577a8c8428fffde98efdf9a03b1d851144dad3c6c265a879156b269256afe","first_computed_at":"2026-07-05T02:02:48.359222Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:02:48.359222Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"JQiNFbYs+rpYfLrvHZ09gHjM82j/n59QtTmQX+iR6hLJBFJqsJAEhYMBsMBHIyOlUuTkgeuqmatmcGwJDYLECQ==","signature_status":"signed_v1","signed_at":"2026-07-05T02:02:48.359611Z","signed_message":"canonical_sha256_bytes"},"source_id":"1502.04939","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3fd79d01a66d9ccd5c0a235c1ef1cc530681b0b0438e5ecee57467cbef3c9af","sha256:ad7a0ce2ae18b52d7033600cbe2e34f7119b26593a00f448e47f3ae2c92d3217"],"state_sha256":"9929b0d667c9a2e1391c3e5dba8d885e8f07ffdd3cf634d28342a196b1eb2bef"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"rIXudCIElxZ/MnEW+ktDJQDbC/DdC3bMyZ8slibdO4Z1RSRnvw21eJPyB2SnelMO0w0Y9d4JlUi9Knf44gE3Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-16T10:59:31.295944Z","bundle_sha256":"9fea390ee9468f578ec6c76943a59db351f08c5610a042852d994efcfce4f317"}}